Voltar para Fibonacci Numbers and the Golden Ratio

4.8

299 classificações

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106 avaliações

This is a course about the Fibonacci numbers, the golden ratio, and their intimate relationship. In this course, we learn the origin of the Fibonacci numbers and the golden ratio, and derive a formula to compute any Fibonacci number from powers of the golden ratio. We learn how to add a series of Fibonacci numbers and their squares, and unveil the mathematics behind a famous paradox called the Fibonacci bamboozlement. We construct a beautiful golden spiral and an even more beautiful Fibonacci spiral, and we learn why the Fibonacci numbers may appear unexpectedly in nature....

Aug 18, 2019

Excellent exposition of a fascinating subject.\n\nVery well organized, including a handout with the course material.\n\nMany thanks to Prof. Chasnov and the HKUST for this worthwhile opportunity!

Mar 23, 2019

Absolutely loved the content discussed in this course! It was challenging but totally worth the effort. Seeing how numbers, patterns and functions pop up in nature was a real eye opener.

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por Peter M

•May 07, 2018

Light, relatively easy and entertaining. Well done Prof. Chasnov

por Vishal G

•Dec 03, 2018

I came into this course thinking that it was going to be something relatively basic - being my first MOOC I wanted to do something which is new but not too difficult so I can see what online courses are like.

The first week is mostly easy but was still interesting with its novel application of recursion to seemingly difficult problems like the staircase one but the second week stands out mostly for both its difficulty and use of other areas of math to prove results in far better ways - Cassini's identity with the Q matrix in particular. The second week's content is manageable and the entire course only requires understanding of mathematical induction and the manipulation of matrices, both of which have supplementary material to complement the course for those who don't know it or have forgotten how to do it. The exercises set are some of the most insightful I've seen - Catalan's identities proof in particular. Solving that one is worthy of commendation. A system of hints or solutions may be useful for the more difficult exercises like that one but it's mostly an exception among the others. The second week is mostly isolated to the others, mostly for the introduction of useful algebraic results which tie Fibonacci numbers together rather than for the end goal which is outlined in week 3 with the construction of the Fibonacci and golden spirals. I personally found week 2 the best but week 3 was the main part of the course. It stays mostly easier than week 2 except the difficulty spike in the first exercise about the Eye of God, I recommend watching the video which comes after it before attempting that exercise.

Overall, this is an enjoyable course with some very surprising results and manages to go deeper into seemingly simple concepts like the Fibonacci numbers than expected. Thanks Professor Chasnov for a great first course which is definitely suitable to beginners with the way it eases students into the concepts introduced and the great explanations. Recursion in particular is explained extremely well.

por Rajeshree D

•Jan 28, 2019

best

por Massimo C

•Jan 17, 2019

Fascinating course about a topic that is not usually taught in maths lessons. It is easy to follow and it has good supporting material.

por Boudokhane M

•Jan 24, 2019

This course has been really fun and informative. I have learned a lot about Fibonacci numbers which i never considered to be that important. At first i thought they were just some quirky numbers and never looked further because they are usually just mentioned in our regular courses but nothing more. This course showed how important they are, their occurrence in nature, their real world application and a multitude of ways to find them and represent them.

The format of this course was also excellent, the videos are rich in content but still entertaining and easy to follow, some of the later ones are worth watching several times because they are quite packed in information. The problems are both challenging and amusing.

overall, i'm really satisfied with this course and i would definitely recommend it to anyone interested in math.

por Bill C

•Sep 03, 2018

Really enjoyed the course. The instructor makes the material very interesting and explains the Fibonacci numbers and their different identities and uses very clearly and easy to understand. The course gave me a better understanding of the Fibonacci numbers and their applications than I previously had. The course also made me think the mathematics through thoroughly and carefully. Highly recommended.

por Rishabh J

•Aug 28, 2018

This is a very good course to introduce Fibonacci numbers, their appearances in nature, and their fascinating properties. The instructor explains everything very well, and his overall speed of teaching is also quite flexible and aptly manged. The course can serve as a good one to introduce one to the idea of advanced mathematics, or to assist one to appreciate the intricate ways in which mathematics appears in the nature.

por Chi L L

•May 13, 2018

The course is a fun one and do make me reflect on my on academic major.

por GOPIKRISHNA

•Jun 21, 2018

Good explanation, Good example

por Bader A

•Dec 24, 2016

This course shows how mathematics is beautiful and fun

por Tumul K

•Jul 04, 2017

A thoroughly enjoyable course, a bit too fast paced and quite difficult some times, but the overall course is quite exciting.

por Eric B

•May 31, 2017

Thanks for this course ! Merci pour ce cours instructif, agréable et complet.

por Dmitry G

•Nov 13, 2017

Beautiful and famous... and it is a math! :)

por Javier G

•Feb 14, 2017

An amazing course

por Andrew M

•Jun 23, 2018

Very clear exposition, interesting and fun. Accessible to anyone interested in maths and patterns.

por Himanshu S

•Sep 13, 2016

Very intriguing and interesting lectures. These got me thinking and venture into Fibonacci numbers and a bit of sacred geometry too.

por Lau C C C

•Apr 21, 2018

thank you very much

por Chavah T

•Feb 13, 2018

Excellent! One of the best classes I've seen on Coursera. Very interesting and lots of fun.

por Bheemarasetty r v s s

•Jun 06, 2018

fun course,great.

por Dmitry S

•Dec 12, 2016

Excellent topic and clear explanations.

por Amith N

•Jan 30, 2017

Neatly planned with excellent information!

por Jill M

•Apr 25, 2018

Excellent! Interesting, informative, clearly presented, and beautifully done!

por Fabrizio B

•Dec 22, 2017

Great course

por Abushieba A I

•May 29, 2017

It's very nice and I had fun!

por Marcin W

•Nov 18, 2016

Very nice course, interesteing approach and examples.

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